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1.89 notes that for a function f, the left and right adjoints of the pullback of f, f! and f* respectively, have very natural interpretations. It would be helpful for me, at least, to show that these, as defined in 1.89, are indeed left and right adjoints.

Further questions: does the procedure for generating f! and f* generalize to pullbacks outside of the category of sets?

## Comments

Hi, Reuben! I've copied your questions here, and will answer them there.

`Hi, Reuben! I've copied your questions [here](https://forum.azimuthproject.org/discussion/comment/17254/#Comment_17254), and will answer them there.`